Evaluation of mixed mode I/II fracture toughness of C 50/60 from Brazilian disc test

S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 119 Focused on Mechanical Fa igue o Me als E alua ion o mixed mode I/II ac u e oughness o C 50/60 om B azilian disc es S anisla Sei l, Pe Mia ka B no Uni e si y o Technology, Facul y o Ci il Enginee ing, Ins i u e o S uc u al Mechanics, Ve eří 331/95, 602 00 B no, Czech Republic [email p o ec ed], h p://o cid.o g/0000-0002-4953-4324 [email p o ec ed] ABSTRACT. Du abili y and sus ainabili y o s uc u es made om conc e e like ma e ials is ge ing mo e in o an in e es o ci il enginee s. S uc u es a e subjec ed no only o uniaxial load, his means i he e is a c ack inside he load could be di ided in o mode I and shea mode II, bu also o a mixed mode I/II. The e o e, i is necessa y o pe o m es , which co e s mixed mode loads and could be used o specimen made om conc e e co e-d ill. Recommended es specimens used o e alua ion o ac u e mechanical pa ame e s has usually a p isma ic o ec angula shape. The cos o eshaping cylinde in o ec angula is expensi e and no e y e icien , he e o e i is e y e ec i e o use B azilian disc es specimen wi h cen al no ch o ob ain mixed mode ac u e pa ame e s. The con ibu ion deals wi h nume ical suppo o B azilian disc es o ob ain calib a ion cu es o mode I and mode II, e alua ion o expe imen al esul s and compa e hem wi h da a adap ed om li e a u e. KEYWORDS. F ac u e Mechanics; F ac u e Toughness; Cen ally C acked B azilian disc; Mixed Mode I/II; Conc e e. Ci a ion: Sei l, S., Mia ka, P., E alua ion o mixed mode I/II ac u e oughness o C 50/60 om B azilian disc es , F a u a ed In eg i à S u u ale, 42 (2017) 119-127. Recei ed: 12.06.2017 Accep ed: 16.06.2017 Published: 01.10.2017 Copy igh : © 2017 This is an open access a icle unde he e ms o he CC-BY 4.0, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. INTRODUCTION oday’s ends in ci il enginee ing pushes in es o s and owne s o conc e e s uc u es mo e o en in o eno a ion, han in o demoli ion o s uc u es. This ac leads in o need o knowledge o ma e ial cha ac e is ics such as bulk densi y, Young’s modulus o elas ici y [1], comp essi e s eng h [2], lexu al s eng h [3], e c. Some ypes o ci il enginee ing s uc u es a e subjec ed o mixed mode loading I and II, he e o e he knowledge o ac u e mechanical pa ame e s is necessa y o p edic li e- ime o conc e e s uc u es (b idges, cooling owe s). To ob ain ma e ial sample om conside ed s uc u e, a co e-d ill is used, which d ills ou a cylind ical sample om a s uc u e. This specimen is es ed o ob ain mechanical p ope ies, bu no o ac u e mechanical pa ame e s. T S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 120 F ac u e mechanical pa ame e s o cemen i ious ma e ials a e usually ob ained om ecommended es s such as: h ee-poin (3PBT) and ou -poin (4PBT) bending es wi h no ch in es ed specimen [4], o mixed mode load [5], wedge spli ing es (WST) [6-9], o a combina ion o WST/3PBT [10] and modi ied compac ension es (MCT) [11, 12]. All es s ha e a p ede ined p isma ic geome y and using hem on specimens made om he co e-d ill is expensi e and no e y e icien , he e o e i is e y app op ia e o use a B azilian disc es specimen wi h cen al no ch (ci cle cu om he co e-d ill cylinde ) [13-16] o de e mina e ac u e pa ame e s o building ma e ials see Fig. 1. Figu e 1: Geome y o a ypical B azilian disc specimen wi h load posi ion alongside c ack. The main ad an age o B azilian disc is, ha i could be used o in es iga ion o ac u e oughness o mode I, mode II and mixed mode by o a ing he c acked agains he load posi ions. This a icle compa es he measu ed expe imen al da a wi h da a p esen ed in [17]. THEORETICAL BACKGROUND Mechanical p ope ies he unno ched B azilian disc is e y o en used as an indi ec es o de e mina e ensile s eng h o ock ma e ials, he e o e i is e y aluable o use i o ob ain ensile s eng h o conc e e [18]. The ensile s eng h can be e alua ed om ollowing equa ion: 2 P DB    (1) whe e  is ensile s ess, P is comp essi e load, D is diame e o disc and B is specimen’s hickness. F ac u e Mechanics This con ibu ion is based on a linea elas ic ac u e mechanics. The linea elas ic ac u e mechanics concep uses he s ess ield in he close icini y o he c ack ip desc ibed by Williams’s expansion [19]. This expansion is an in ini e powe se ies o iginally de i ed o a homogenous elas ic iso opic c acked body, which can be desc ibed by a ollowing equa ion: ,() () (,) III III i j ij ij ij KK O      (2) whe e  ij ep esen s he s ess enso componen s, KI, KII is he s ess in ensi y ac o o mode I espec i ely mode II, Iij, IIij, a e known shape unc ions o mode I and mode II, Oij ep esen s highe o de e ms and , θ a e he pola coo dina es (wi h o igin a he c ack ip; c ack aces lie along he x-axis). T S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 121 The alues o he s ess in ensi y ac o (SIF) o a ini e specimen and he pola angle θ = 0° can be exp essed in he ollowing o m [20-22]: (/ , ) II Pa K aR RB    (3) (/ , ) II II Pa K aR RB    (4) whe e P is comp essi e load, a is a c ack leng h, R is adius o he disc (D/2), B is disc hickness and I(a/R, ), II(a/R, ) a e dimensionless shape unc ions (calib a ion cu es) o mode I and mode II, see Figs. 2 and 3. NUMERICAL MODEL Calib a ion cu es o ob ain igh calib a ion cu es o each mode o SIF a nume ical simula ion was necessa y. The nume ical simula ion was pe o med in ini e elemen (FE) so wa e Ansys 17.2 [23]. A wo-dimensional (2D) nume ical model wi h plane s ain bounda y condi ion we e used o calcula e SIF (KI and KII). The nume ical model was meshed wi h elemen ype PLANE183 aken om ANSYS’s elemen s lib a y and command KSCON was used o ake in o accoun he c ack ip singula i y. Inpu ma e ial p ope ies o conc e e used in FE so wa e a e ollowing: Young’s modulus and Possion’s a io, E = 40 GPa and ν = 0.2, espec i ely. The geome y o disc has adius R = 50 mm and he ela i e c ack leng h a/R a ied om <0.1; 0.9>, no ch angle α a ied <0°; 90°> and was loaded wi h cons an o ce P = 100 N in all calcula ed cases. In FE so wa e ANSYS, he ollowing equa ions a e used o calcula ion o he SIF KI and KII o θ = ±180. 2 21 I G K     (5) 2 21 II u G K     (6) whe e u, a e nodal displacemen s, G shea modulus,  is Koloso ’s cons an o plane s ain espec i ely plane s ess condi ions and is coo dina e in cylind ical coo dina e sys em. F om B azilian disc geome y, men ion abo e a calib a ion cu es o mode I and II o a ious no ch angle  and a/R a io can be de e mined as a ollowing unc ions [25, 26]: (/ , ) 1 I I KRB a aR R Pa    (7) (/ , ) 1 II II KRB a aR R Pa    (8) F om Fig. 2, i can be no iced, ha o some angle  and a/R, he alue o calib a ion cu e o mode I equals ze o ( I(a/R,) = 0). This means, ha he e is only mode II (pu e shea mode). The e o e, he ac u e oughness o mode II could be e alua ed. T S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 122 Figu e 2: Calib a ion cu e I(a/R,) o mode I. Figu e 3: Calib a ion cu e II(a/R, α) o mode II. EXPERIMENT FOR MATERIAL C 50/60 Ma e ial a e ial used in he expe imen al p og am was s anda d conc e e C 50/60, maximum agg ega e size was 8 mm. Specimen’s geome y B azilian disc specimens we e p epa ed om s anda dized cylind ical specimens used o e alua ion o cylind ical comp essi e s eng h o conc e e [2]. No ches we e p epa ed by using wa e je cu e . The dimensions o specimens a e in oduced in Tabs. 1 and 2. Specimen nm . Diame e D [mm] Thickness B [mm] 04 150 28.59 05 150 30.52 06 150 29.90 Table 1: Dimensions o B azilian disc specimens. M S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 123 Specimen nm . a/R [-] Diame e D [mm] Thickness B [mm] No ch leng h a [mm] 05_4 0.2667 150 31.83 40.06 09_4 0.2667 150 30.68 40.00 04_4 0.2667 150 31.65 40.09 09_6 0.4 150 29.93 60.17 01_6 0.4 150 31.44 60.92 04_6 0.4 150 30.97 60.15 07_6 0.4 150 31.17 59.94 Table 2: Dimensions o B azilian disc specimens wi h a cen e no ch. Expe imen al p ocedu e The machine o es s was Seidne D7940 wi h maximum loading capaci y 4 000 kN. The load a e was 0.01 kN/s. B azilian disc specimens wi hou no ch we e es ed o ob ain he ensile s eng h. B azilian disc specimens wi h he no ch we e es ed unde he selec ed angles inclined agains loading posi ions see Tab. 3. Figu e 4: Example o specimens used o B azilian disc es wi hou and wi h no ch Specimen nm . a/R [-] Inclina ion angle  [°] 05_4 0.2667 0.0 09_4 0.2667 10.0 04_4 0.2667 27.2 09_6 0.4 0.0 01_6 0.4 0.0 04_6 0.4 10 07_6 0.4 25.2 Table 3: The ela i e leng h o no ch in B azilian disc specimens and angle o used angle posi ion. S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 124 RESULTS AND DISCUSSION Selec ed ma e ial and mechanical p ope ies nno ched B azilian disc specimens we e subjec ed o comp essi e load o e alua e ensile s eng h om Eq. 1. The measu ed o ces and calcula ed ensile s eng h a e showed in Tab. 4. Specimen nm . Measu ed o ce P [kN] Tensile s eng h [MPa] 04 34.9 5.18 05 38.8 5.39 06 35.7 5.06 Table 4: Measu ed o ces and calcula ed ensile s eng h om eq. (1) o unno ched B azilian disc. The p ope ies o used conc e e a e compa ed wi h ma e ial cha ac e is ics o mo a and conc e e om Hou [17], o de ailed in o ma ion abou composi ion o hese ma e ials see [17]. Compa ison o selec ed mechanical p ope ies is showed in Tab. 5. Bulk densi y ρ [kgm-3] Comp essi e s eng h c [MPa] Tensile s eng h [MPa] Mo a om [17] 2018 25.56 3.6 Conc e e [17] 2373 34.42 3.1 Conc e e – p esen s udy 2321 55.4 5.21 Table 5: Compa ison o selec ed mechanical cha ac e is ics o used conc e e wi h da a adap ed om li e a u e [17] F ac u e mechanical p ope ies F ac u e mechanical p ope ies o s uc u al conc e e we e e alua ed om Eq. (2) and (3). The alues o s ess in ensi y ac o s we e e alua ed o mode I (specimens 05_4,09_6 and 01_6), o mode II (specimens 04_4 and 07_6) and o mixed mode I/II. The e alua ed ac u e mechanical p ope ies a e summed up in Tab. 6. Specimen nm . Measu ed o ce P [kN] KI [MPamm1/2] KII [MPamm1/2] 05_4 26.8 38.069 0.0006 09_4 24.3 30.513 25.906 04_4 25.2 0.0466 54.604 09_6 19.6 36.858 0.0012 01_6 20.0 35.784 0.0012 04_6 17.7 26.104 25.337 07_6 15.8 0.005 44.9745 Table 6: Measu ed expe imen al load P and calcula ed ac u e mechanical pa ame e s KI and KII o each specimen. U S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 125 Figu e 5: Compa ison o ac u e esis ance KII/KIC (y axis) agains KI/KIC (x axis) beha io wi h da a om li e a u e [17]. Compa ison o expe imen al da a Expe imen al esul s om Hou [17] we e digi alized and measu ed o ces we e used o be compa ed wi h da a measu ed in he p esen ed s udy. The compa ison o esul s is done in wo ways. The i s one compa es ac u e esis ance alues o KII/KIIC (y axis) agains KI/KIC (x axis) which is aluable o see pu e mode I and pu e mode II ac u e esis ance. An en elope cu e (a ci cle wi h adius KI/KIC = 1 and KII/KIIC = 1) is plo ed in Fig. 5. o see e ec o mixed mode I/II ailu e o each es ed specimen (di e en inclina ion angle  o no ch). The compa ison made in Fig. 4. is no e y o en, he e o e i is being necessa y o made compa ison which can be usually seen in li e a u e. Fig. 5 compa es no ma i e alues o KII/KIC (y axis) agains KI/KIC (x axis) which is aluable o see mode II e ec s ac u e esis ance. An en elope cu e (an ellipse wi h adius KII/KIC = mean alue and KI/KIC = 1) is plo ed in Fig. 6. o see e ec o mixed mode ailu e o each es ed specimen (di e en inclina ion angle o no ch). Figu e 6: Compa ison o ac u e esis ance KII/KIC (y axis) agains KI/KIC (x axis) beha io wi h da a om li e a u e [17]. S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 126 CONCLUSIONS he p esen pape aims a analyzing he mixed mode ac u e in a conc e e C50/60 using he B azilian disc es . A ini e elemen analysis o B azilian disc specimen, e ec s o c ack angle o a ion a e s udied based ac u e mechanic app oach. The ollowing p incipal conclusions could be de i ed:  The classical solu ions o Linea Elas ici y o he s ess ields in he neighbo hood o a c ack ip in pu e mode I o II can be ob ained independen ly  The solu ion o he s ess ield in a combined mode si ua ion is ob ained simply by o a ion o a ini ia ion c ack.  Expe imen ally ob ain da a o C 50/60 is compa ed wi h da a om li e a u e. The p esen ed nume ical calcula ion and expe imen al esul s (C 50/60) will be used o u u e wo-pa ame e ac u e e alua ion on alkali ac i a ed conc e e [27, 28]. ACKNOWLEDGMENT his pape has been wo ked ou unde he “Na ional Sus ainabili y P og amme I” p ojec “AdMaS UP – Ad anced Ma e ials, S uc u es and Technologies” (No. LO1408) suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech Republic. REFERENCES [1] ISO 1920-10, Tes ing o conc e e – Pa 10: De e mina ion o s a ic modulus o elas ici y in comp ession, (2015). [2] EN 12390-3, Tes ing ha dened conc e e – Pa 3: Comp essi e s eng h o es specimens, (2009). [3] EN 12390-5, Tes ing Ha dened Conc e e –Pa 5: Flexu al S eng h o Tes Specimens. Eu opean Commi ee o S anda diza ion, (2009). [4] RILEM Repo 5, F ac u e Mechanics Tes Me hods o Conc e e Edi ed by S. P. Shah and A. Ca pin e i, Chapman and Hall London, (1991). [5] Maliko a, L., Vesely, V., Sei l, S., C ack p opaga ion di ec ion in a mixed mode geome y es ima ed ia mul i- pa ame e ac u e c i e ia, In e na ional Jou nal o Fa igue, 89 (2016) 99–107. DOI: 10.1016/j.ij a igue.2016.01.010. [6] Linsbaue , H., Tschegg, E., F ac u e ene gy de e mina ion o conc e e wi h cube-shaped specimens, Zemen Be on, 31 (1986) 38–40. [7] B ühwile , E., Wi mann, F. H., The Wedge Spli ing Tes , a New Me hod o Pe o ming S able F ac u e Mechanics Tes , Enginee ing F ac u e Mechanics 35 (1990) 117–125. [8] Sei l, S., Veselý, V., Řou il, L., Two-pa ame e ac u e mechanical analysis o a nea -c ack- ip s ess ield in wedge spli ing es specimens, Compu e s and S uc u es 89(21-22) (2011) 1852–1858. DOI: 10.1016/j.comps uc.2011.05.020. [9] Sei l, S., Nie o Ga cía, B., Me a I., Wedge spli ing es me hod: Quan i ica ion o in luence o glued ma ble pla es by wo-pa ame e ac u e mechanics, F a u a ed In eg i a S u u ale, 30 (2014) 174–181. DOI: 10.3221/IGF-ESIS.30.23. [10] Sei l, S., Ko e, S., De Co e, W., Boel, V., Sobek, J., Veselý, V., Selec ing a sui able specimen shape wi h low cons ain alue o se e mina ion o ac u e pa ame e s o cemen i ious composi es, 577–578 (2014) 481–484. DOI: 10.4028/www.scien i ic.ne /KEM.577-578.481. [11] Sei l, S., Viszlay, V., Modi ied compac ension specimen o expe imen s on cemen based ma e ials: Compa ison o calib a ion cu es om 2D and 3D nume ical solu ions, F a u a ed In eg i a S u u ale, 11(39) (2017) 118–128. [12] Sei l, S., Ríos, J.D., Ci uen es, H., Veselý, V., E ec o he load eccen ici y on ac u e beha io o cemen i ious ma e ials subjec ed o he modi ied compac ension es , Solid S a e Phenomena, 258 SSP (2017) 518–521. DOI: 10.4028/www.scien i ic.ne /SSP.258.518. [13] Li, D., Wong, L. N. Y., The B azilian disc es o ock mechanics applica ions: e iew and new insigh s, Rock mechanics and ock enginee ing, 46(2) (2013) 269–287. DOI: 10.1007/s00603-012-0257-7. [14] A kinson, C., Smelse , R. E., Sanchez, J., Combined mode ac u e ia he c acked B azilian disk es . In e na ional Jou nal o F ac u e, 18(4) (1982) 279–291. T T S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13 127 [15] Abshi ini, M., Sol ani, N., Ma ashizadeg, P., On he mode I ac u e analysis o c acked B azilian disc using a digi al image co ela ion me hod. Op ics and Lase s in Enginee ing, 78 (2016) 99–105. DOI: 10.1016/j.op laseng.2015.10.006. [16] Aya ollahi, M.R., Aliha, M.R.M., C acked B azilian disc specimen subjec ed o mode II de o ma ion, Enginee ing F ac u e Mechanics, 72 (2005) 493–503, DOI: 10.1016/j.eng acmech.2004.05.002. [17] Hou, Ch., Wang, Z., Liang, W., Li, J., Wang, Z., De e mina ion o ac u e pa ame e s in cen e c acked ci cula discs o conc e e unde diame al loading: A nume ical analysis and expe imen al esul s, Theo e ical and applied ac u e mechanics, 85 B (2016) 355-366. DOI: 10.1016/j. a mec.2016.04.006. [18] ISRM (1978) Sugges ed me hods o de e mining ensile s eng h o ock ma e ials, In J Rock Mech Min Sci Geomech Abs , 15 (3) (1978) 99–103. DOI:10.1016/0148-9062(78)90003-7. [19] Williams, M. L., On he s ess dis ibu ion a he base o a s a iona y c ack. ASME Jou nal o Applied. Mechanics, 24 (1957) 109–114. [20] Ande son, T. L., F ac u e mechanics: Fundamen als and applica ions. Taylo & F ancis g oup, (2005). [21] Pook, L. P., Linea Elas ic F ac u e Mechanics o Enginee s: Theo y and Applica ions. Uni e si y College London, Uni ed Kingdom, (2000). [22] Aya ollahi, M. R., Pa ie , M. J., Smi h, D. J. De e mina ion o T-s ess om ini e elemen analysis o mode I and mixed mode I/II loading. In e na ional jou nal o ac u e, 91(3) (1998) 283-298. [23] Aya ollahi, M.R., Aliha, M.R.M., On he use o B azilian disc specimen o calcula ing mixed mode I–II ac u e oughness o ock ma e ials, Enginee ing F ac u e Mechanics, 75 (2008). 4631–4641. DOI: 10.1016/j.eng acmech.2008.06.018. [24] ANSYS®, Academic Resea ch, Release 17.2, Help Sys em, C ack analysis guide. Mechanical APDL Documen a ion Guide, ANSYS, (2016). [25] Tada, H., Pa is, P.C., I win, G.R., The s ess analysis o c ack handbook, hi d edi ion, The Ame ican socie y o mechanical enginee ing. New Yo k, (2000). [26] Hae i, H., Shah ia K., Fa ehima ji. M., Moa e and, P., On he c ack p opaga ion analysis o ock like B azilian disc specimens con aining c acks unde comp essi e line loading. La in Ame ican jou nal o solids and s uc u es, 11(8) (2014) 1400–1416. [27] Bílek, V., Hu a, J., Done, P., Zidek, L., De elopmen o alkali-ac i a ed conc e e o s uc u es-Mechanical p ope ies and du abili y, Pe spec i e in Science, 7(2016) 190–194. DOI: 10.1016/j.pisc.2015.11.031 [28] Bílek, V., Bonczko á, S., Hu a, J., Py lík, D., M o ec, M., Bond s eng h be ween ein o cing s eel and di e en ypes o conc e e, P ocedia Enginee ing, 190 (2017) 243–247. DOI: 10.1016/j.p oeng.2017.05.333.